25B07
A General Analysis of Electric Probes:
Deduction of Mach Number and Plasma Density in Complex Plasmas.
Kyu-Sun Chung1, H.J. Woo1, E.K. Park1, Y.S. Choi2, T. Lho1,2, S. Kado3, S. Kajita4, and N. Ohno4
1. Department of Electrical Engineering & Center for Edge Plasma Science, Hanyang University, Korea
2. Division of Plasma Applications, National Fusion Research Institute, Korea
3. Department of Quantum Engineering & Systems Science, The University of Tokyo, Japan
4. Department of Energy Engineering & Science, Nagoya University, Japan

A single electric probe is used to deduce the electron temperature and plasma density, and a Mach probe(MP) is for the deduction of Mach number. However, the deduced plasma density or Mach numbers would
be severely different from those by collisionless models if plasma were in the complex conditions withmagnetic field, various atomic processes would be necessary by including these parameters. A typical MP
is composed of two directional electric probes located at opposite sides of an insulator, which is mostly
used as a parallel MP, but there are other MP's such as perpendicular MP (PMP), rotating (Mach) probe(RP), Gundestrup probe (GP), and visco-MP (VMP), depending upon the shape of the probe holder,
location of different probes, or the way of collecting ions. Existing theories of parallel Mach probes in
un-magnetized and magnetized flowing plasmas are introduced in terms of kinetic, fluid andparticle-in-cell models along with key physics and comments. Experimental evidences of relevant models
are shown along with validity of related theories, which have been partially performed in the linear divertor
simulators. Deduced data of tokamak experiments are to be re-evaluated especially for the collisional
cases. Error analysis is to be given. For the probes other than the typical parallel Mach probe (MP), the) canrelation between the ratio of ion saturation currents and normalized drift velocity (be expressed as a combination of the functional forms: Exponential and/or polynomial form offor PMP; Incident angle of magnetic field, cross-field flow velocity and ratio(R) of ion
saturation currents of MP for RP and GP; Two R's of separate two MP's for VMP. Collisions ofion/electron/neutrals, asymmetries of ion temperatures and existence of hyper-thermal electrons, existenceof ion beam, supersonic flow and negative ions can affect the deduction of the flow velocities by MP.

1.Introduction
Although the current issue of fusion science isto check the engineering feasibility of fusion energy
via ITER (International Tokamak ExperimentReactor), the basic scientific problems are still to beunderstood, among which the problems ofplasma-material interactions via the edge localized
modes (ELM) and flow related phenomena, andthese are very similar to the analyses of the various
electric probes.
Generally using collisionless probe theories, asingle electric probe is used to deduce the electron
temperature and plasma density, and a Mach probe
is for the deduction of Mach number. However, thededuced Mach numbers or density would beseverely different from those by collisionlessmodels if plasma were in the complex conditions
with magnetic field, various atomic processes
would be necessary by including these parameters.
A Mach probe (MP) is an electric probe system
to deduce the plasma flow velocity from the ratio of
the ion saturation currents. Generally, a typical MP
is composed of two directional electric probes
located at opposite sides of an insulator, which ismostly used as a parallel MP, but there are otherMP's such as perpendicular MP (PMP), Gundestrup
probe (GP) or rotational probe (RP), and visco-MP(VMP), depending upon the shape of the probe
holder, location of different probes, or the way ofcollecting ions.
From this brief review, existing models for thededuction of flow velocity and density are to besummarized in the collisional plasmas andcompared with those in the collisionless ones.
Experiments in the simulated divertor devices will
be given using not only electric probes but aloslaser-aided diagnostics.
2.Models
For the parallel MP, the relation between the ratioof the upstream ion saturation current density (Jup)to the downstream (Jdn) and the normalized drift
velocity () of plasma has generallybeen
fittedintoanexponential
form. For the GP or RP,
withobliqueioncollection,, where K is a calibration

factor ~ 2.4,,
is normalized
perpendicular flow to the magnetic field, and θ isthe angle between the magnetic field and probesurface. Normalized drift velocity of the flowing
plasmas is deduced from the ratio (Rm) measured by. Existing theories ofan MP asMach probes in un-magnetized and magnetizedflowing plasmas are introduced in terms of kinetic,
fluid and particle-in-cell models or self- andself-similar methods along with key physics andcomments. For the probes other than the typicalparallel Mach probe (MP), the relation between theratio of ion saturation currents andcan beexpressed as a combination of the functional forms:
for
Exponential and/or polynomial form of
PMP; Two R 's of separate two MP's for VMP.
Collisions of ion/electron/neutrals, asymmetries ofion temperatures and existence of hyperthermal
electrons, existence of ion beam, supersonic flow
and negative ions can affect the deduction of theflow velocities by MP. Since the ion saturation
current density is dependent upon the magnetic
field, collisionality and charge states of the plasmas,
the deduced density of the unperturbed plasmas
should be changed accordingly, if one-directional
electric probe is used. If one uses a spherical,
cylindrical or planar probe exposing two sides (orall sides) of the probe to the plasma, flow effectcould be canceled while other effects is still valid.
3. ExperimentTo establish and confirm the method of deductionof Mach numbers and densities, one needs not only
to develop the physical model but also to verify themodel by the independent diagnostics such as
laser-induced fluorescence (LIF) and laser Thomson
scattering (LTS) methods. Proper provision ofelectron temperature is the sufficient condition forthe deduction of absolute flow velocity for all flow
measurement, especially for the case of collisional
plasmas, since almost all the existing probe theories
are for the case of collisionless and stationary
plasmas. To resolve these complex problems, LIF
and LTS methods are to be introduced with electricprobe measurement for the measurement of plasma
flow and plasma parameters in the weakly
magnetized collisonal plasmas generated at theDivertor Plasma Simulator (DiPS).
Plasma isgenerated by LaB6 cathode discharge withmagnetic field of 500 - 2000 Gauss. For the wide
rangeofcollisionality,
plasmadensityand electron temperature
are measured by a single electricprobe using a conventional collisionless probe

theory. To check the effect of collisionality andmagnetic field on the flow, density and temperature,various electric probes (single, triple and Machprobes) and laser (LIF and LTS) systems have been
installed. Based upon previous modeling of theneutral effect, ion-neutral collision is considered as
most dominant effect on the change of ion
momentum among various atomic effects such asrecombination and ionization. Variations of Mach
number and plasma density with collisionlessmodels are to be compared with those by collisonalmodels for different pressures which indicates that
the Mach numbers by the collisionless model are
overestimated by 50 % - 100 %. Data of Machprobe has been compared to those by LIF and thoseof SP are compared to those by LTS, and data ofvarious linear divertor simulators such as MAP-2 ofUniversity of Tokyo and NAGDIS-2 of Nagoya
University have been shown to compare with thoseof DiPS. Deduced plasma densities with flow andpressure are also to be presented.
4.SummarySingle probe and Mach probes(Parallel Machprobe(MP), perpendicular MP, rotating Mach probe,
Gundestrup probe, and visco-MP) are analyzed bycomparing existing theories in un-magnetized andmagnetized flowing plasmas in terms of kinetic,
fluid and particle-in-cell models along with key
physics and comments. Experimental evidences ofrelevant models are shown along with validity ofrelated theories. Deduced data of tokamak
experiments are re-evaluated for the collisionaledge conditions.
Acknowledgments
This research was supported by National R&D
Program through the National Research Foundationof Korea (NRF) funded by the Ministry ofEducation, Science and Technology (2011 0018734), and partially supported by the National
Fusion Research Institute.
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